General Relativistic MHD Simulations of Jet Production

Y.Mizuno (NSSTC/MSFC/NRC)

CollaboratorsK.-I. Nishikawa (NSSTC/UA), P. Hardee(UA),

S. Koide (Toyama Univ.), K. Ghosh (NSSTC/USRA)G.J. Fishman (NASA/MSFC)

Introduction

• Relativistic jets have been observed in AGNs, microquasars and GRBs, and it is believed that they originate in the region near the black hole.

• Magnetic accretion model is one of the promising model for the jet formations.

• Recent long-term MHD simulations for the evolution of accretion disk show the turbulent and complex structures in accretion disk by the non-axisymmetric growth of magneto-rotational instability

Global 3D MHD simulations of black hole accretion disk

(Machida & Matsumoto 2003)• They have performed 3D non-relativistic MHD simulations of geometrically thick accretion disk with toroidal magnetic fields.•After the non-axisymmetric MRI grows, the disk region becomes turbulent.• Magnetic field lines are less turbulent and globally show a bisymmetric spiral shape.• One-armed spiral mode dominates in the density distribution.• The formation of non-axisymmetric structure is a general picture for the accretion disk.

density Magnetic field line

3D MHD simulations of jets from accretion disk (Kigure & Shibata 2005)

• They have performed non-relativistic MHD simulations of a jet formation by the interaction between an accretion disk and a large scale magnetic field including non-axisymmetric modes (sinusoidal (m=4) and random perturbation into rotation velocity of disk)• They found the formed jet have non-axisymmetric structure with m=2 in both of cases• The non-axisymmetric structure in the jet originates in the accretion disk, not in the jet itself.

Sinusoidal

random

Purpose of Present Study

• We investigate the connection between the non-axisymmetric structure in the jet and that in the disk based on GRMHD simulations

• We compare the characteristics of jets found in 3D non-relativistic MHD simulations.

4D General Relativistic MHD Equation

• General relativistic equation of conservation laws and Maxwell equations: 　　　

　　　　　　　∇ ( n U ) = 0 　　　 (conservation law of particle-number)

　　　　　　　∇ T = 0 (conservation law of energy momentum)

　　　　　　　∂ F∂F∂F = 0

　　　　　　　∇ F = - J

• Frozen-in condition: FU= 0

• metric ：　 ds2 = gdxdx;

g= - h02 ; gii= - hi

2 ;

　　 g0i= - hi2i (i=1,2,3) ; gij= 0 (i≠j)

n: proper particle number density. p : proper pressure. c: speed of light.e : proper total energy density, e=mnc2 + p / ( -1).; Γ=5/3 m : rest mass of particles. : specific heat ratio.U : velocity four vector. A : potential four vector. J : current density four vector.∇ : covariant derivative. g : metric.

T : energy momentum tensor, T = pg + (e+p)UU+FF -gF

F/4.F : field-strength tensor, F =∂ A -∂A

(Maxwell equations)

We neglect the evolution of metric and the essential micro physics (we use gamma-law EOS)

Vector Form of General Relativistic MHD Equation

(3+1 Formalism) 　

σPfPTP

:)()]([ curv2

2

c

cDc

t

)]([ Hvv

Dt

D

σTPvvP :)()]([ 222H

cDcct

)( BβEB

ct

Eβ

BE

βJctc

c 2e

1

0B E2e

1

c

0BvE Where

βv cH

3

1curv

j

jjji

ijij

i TGTGf ji

jiij x

h

hhG

1

(conservation law of particle-number)

(equation of motion)

(energy equation)

(Maxwell equations)

(ideal MHD condition)

: (Lapse function)

ji

j

iij xh

h

c

h iii : (shift vector)23

1

20

i

ii

c

hh

general relativistic effect

special relativistic effect

: (shift velocity)

Special relativistic mass density,

Special relativistic total momentum density

Special relativistic total energy density

D: densityP: momentum densityT: energy-momentum tensor: energy density

Simulation Model of Jet formation• Numerical code

– 3D general relativistic MHD code (Koide et al. 2000; Koide 2003; Mizuno et al. 2005)

• Initial condition– Geometrically thin accretion disk (d/c=10

0) rotates around the rotating black hole (a=0.95)

– The back ground corona is free-falling to a black hole (Bondi solution)

– The global vertical magnetic field (Wald solution; B0=0.1 (c2)1/2)

– Input the sinusoidal perturbation (m=5 mode, 15% of Keplerian velocity) into the rotation of the disk (v=0.15VKsin5)

• Numerical Region and Mesh points– 1.0 rS < r < 60 rS, 0< < /2, 0< < 2w

ith 150*64*150 mesh points

Initial condition of simulations Color: denistyWhite lines: magnetic field lines

Time evolution of density(x-z plane (y=0)); Non-perturb case

Color: densityWhite lines: poloidal magnetic filedVector: poloidal velocity

• The matter in the disk loses its angular momentum by magnetic field and falls to the black hole

• A centrifugal barrier decelerates the falling matter and make a shock around r=2rS.

• The matter near the shock region is accelerated by the J×B force and gas pressure and forms relativistic outflows.

Time evolution of density(x-z plane (y=0)); Sinusoidal-perturb case

Color: densityWhite lines: poloidal magnetic filedVector: poloidal velocity

• The general properties are almost same as that of non-perturb case (shock and jet formation).

• Due to the initial perturbation of the disk, the disk structure is slightly different with that of non-perturbation case (thicker and less concentration of density near the black hole)

2D (x-z plane) snapshot of density and Plasma beta

• In both cases, the relativistic jet is formed near the black hole and propagate outward with the twisted magnetic field (torsional Alfven waves)

• The accretion disk becomes geometrically thick near the black hole by the propagation of shock produced by the centrifugal barrier around r=2rS.

• Due to the initial perturbation of the disk, the disk structure is slightly different with that of non-perturbation case (thicker and less concentration of density near the black hole)

Contour B

Time evolution of density and magnetic field

Sinusoidal perturbation case

Time: 0 ~ 120 S (step 5 S) Color contour: density, slice (at equatorial plane and x=0).White curves: magnetic field lines

3D snapshot of density and magnetic field structure

Non-perturbation case (t/S=120) Sinusoidal perturbation case (t/S=114)

• The overall structure of magnetic field is almost same in both of cases (magnetic field near the black hole is strongly twisted and propagate outward).

Time evolution of density and magnetic field into the disk (x-y plane)

Sinusoidal perturbation caseTime: 0 ~ 120 S (step 5S)Color contor: density at z=1.0 rS.White curves: magnetic field lines

• Initial perturbation (m=5) is clearly seen in early stage• Initial perturbation becomes weak by the coupling of accretion matter•High density region (shocked region) show the non-axisymmetric structure clearly (initial m=5 mode and other?).• In late stage, by the coupling them density becomes more complicated structure

2D (x-y plane) plot of density into accretion disk Non-perturbation case (t/S=120) Sinusoidal perturbation case (t/S=114)

• In the sinusoidal perturbation case, the density into the disk show the complex non-axisymmetric structure.• Some part of the non-axisymmetric structure reflects the initial sinusoidal mode (m=5) and some part of that mixes other (lower?) mode.• The initial perturbation of rotation velocity make homogeneity of accretion to the black hole. • Although the homogeneity of accretion becomes weak by the coupling of accretion matter, it still survives and produce other mode by the coupling.

2D (x-y plane) plot of density into jet

• On the other hand, in the jet some non-axisymmetric structure are seen in both of cases, but they are very faint.• The non-axisymmetric structure in the sinusoidal perturbation case reflects the initial sinusoidal perturbation of disk and may mix with other lower mode (is not seen clearly).

Outflow structure

• The outflow has the complicated density and velocity structure.• Especially, the velocity is fast near the rotation axis and gradually decrease with distance from rotation axis and tend to inflow after the transition region. • These inflow/outflow structure become a strong theoretical support to understand the relativistic outflow and/or inflow properties seen in the absorption line spectra of some narrow emission line quasars.

density Total velocity

Out flow structure3D GRMHD, a=0.95, b0=0.1(c2)1/2, non-perturb1D slice along jet (x=5rS, y=0rS)

In the part of jet, density is lower than coronal density

Vtot > Vk and V tot ~ VA

Relativistic radiation transfer

Emission, absorption & scattering

Collaborative works with S.Fuerst and K. Wu (astro-ph/0509601)

• We have calculated the optically thin thermal free-free emission from a disk-outflow system based on the results of our 2D GRMHD simulations.• We consider a covariant radiation transfer formulation (Fuerst & Wu 2004, A&A, 424, 733) and solve the transfer equation using a ray-tracing algorithm.• In this algorithm, we treat general relativistic effect (light bending, gravitational lensing, gravitational redshift, frame-dragging effect etc.).

Relativistic radiation transfer

• The radiation image shows the front side of the accretion disk and the other side of the disk at the top and bottom regions. • It is because the general relativistic effects.

• We can see the propagation of waves and the strong radiation from geometrically thick disk near the BHs.• The jet generated in GRMHD simulation is not visible in the radiation image.• This is because we assume the thermal free-free emission. It has a strong density dependence and the jet is less dense than the disk.• If we calculate the emission with weaker dependence on the density, such as non-thermal process or Compton scattering, the jet would be visible.

Project image of thermal emission (<20 rs)

2D GRMHD simulations (a = 0.95, B = 0.1 (ρc2)-2)

Summary and Discussion

• We have performed 3D GRMHD simulations of the jet formation from the accretion disk with/without the initial perturbation (sinusoidal perturbation) around the rotating black hole.

• Although the initial perturbation of accretion disk becomes weak by the interaction with accretion matter, it survive and affect the disk and jet structure.

• Some other modes are happen in the accretion disk.• Newtonian MHD simulations of jet formation with non-axisymme

tric mode show the growth of m=2 mode but our GRMHD simulations have not seen the clear growth of m=2 mode.

• We have calculated the free-free emission from a disk/outflow near a rotating black hole based on 2D GRMHD simulations using a covariant radiation transfer formulation.

• The calculation shows the propagation of waves and the strong radiation from geometrically thick disk near the black hole.